IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v103y2001i1p161-17310.1023-a1012903105391.html
   My bibliography  Save this article

Global Convergence of Conjugate Gradient Methods without Line Search

Author

Listed:
  • Jie Sun
  • Jiapu Zhang

Abstract

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC 1 objective function; (2) The Polak–Ribière method and the Conjugate Descent method applied to a general, not necessarily convex, LC 1 objective function. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Jie Sun & Jiapu Zhang, 2001. "Global Convergence of Conjugate Gradient Methods without Line Search," Annals of Operations Research, Springer, vol. 103(1), pages 161-173, March.
    • Handle: RePEc:spr:annopr:v:103:y:2001:i:1:p:161-173:10.1023/a:1012903105391
    DOI: 10.1023/A:1012903105391
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1012903105391
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1012903105391?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sun, Jie & Yang, Xiaoqi & Chen, Xiongda, 2005. "Quadratic cost flow and the conjugate gradient method," European Journal of Operational Research, Elsevier, vol. 164(1), pages 104-114, July.
    2. Shao-Jian Qu & Mark Goh & Xiujie Zhang, 2011. "A new hybrid method for nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 49(3), pages 493-520, July.
    3. Shi, Zhen-Jun & Shen, Jie, 2007. "Convergence of Liu-Storey conjugate gradient method," European Journal of Operational Research, Elsevier, vol. 182(2), pages 552-560, October.
    4. Yi-gui Ou & Guan-shu Wang, 2012. "A hybrid ODE-based method for unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 53(1), pages 249-270, September.
    5. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
    6. C. Labat & J. Idier, 2008. "Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 43-60, January.
    7. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:103:y:2001:i:1:p:161-173:10.1023/a:1012903105391. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.